On the Selection of Cellular Automata based PRNG in
Code Division Multiple Access Communications

Abstract: The main contribution of this article is to investigate the application suitability of Cellular Automata based pseudo-random noise generator in Code Division Multiple Access Communications. New dynamics in group Cellular Automata were explored. Extensive analysis for two classes of group Cellular Automata (maximum length Cellular Automata and equal length Cellular Automata) were carried out. The analysis and comparison results for these classes of group Cellular Automata demonstrate the advantages of equal length Cellular Automata over maximum length Cellular Automata in view of code division multiple access applications.

Pseudo-random noise generators (PRNGs) are used in engineering applications such as in built-in self-test (BIST) circuits applications and in the validation of design and manufacturing control. In data security, strength of the crypto-system depends on the quality of PRNGs. In communications, multiple equal length random keys are required in view of code division multiple access (CDMA), where the keys in CDMA should be independent (de-correlated) between them. Application specific requirements resulted in numerous approaches for PRNGs, for example, PRNG designs are available based on Coupled Mapped Lattices (CMLs) [42], Cellular Automata (CAs) [5, 27, 38], and Linear Feed Back Shift Register (LFSRs) [9, 12, 17]. CAs were suggested for potential uses in BISTs and data security applications with advantages of having low cost physical implementation and support for easy incorporation in very-large-scale integration (VLSI) architecture [5, 27].

CAs evolve in discrete space and time. Elementary CAs (ECAs) are 1-dimensional, 3-neighbourhood CAs with fixed or periodic boundary condition [38]. ECA evolutions are dependent on binary values of the CA cells and CA transition functions (total 256 rules, also known as Wolfram CA rules). The next state function (CA rule) of the cell at time is of the present states of , and cell at time t [27]. A CA rule is additive when it involves only XOR and XNOR logic.

A special class of ECAs always producing cycles is referred as group CA. Additive rules play an important role in generation of group CAs. Uses of group CAs as PRNGs were described in [27].

The main purpose of this article is to compare PRNGs based on CAs, LFSRs, and CMLs aiming CDMA applications and to show that a class of ECAs, Equal Length Cellular Automata (ELCAs) is well suited for CDMA applications.

The article is organized as follows: PRNGs based on LFSRs, CMLs, and CAs are compared in Section 2; Section 3 introduces the analysis of CA based PRNGs in all fixed boundary conditions; while properties related to CA based PRNGs are discoursed in Section 4. Discussion and conclusions are followed in Section 5 and Section 6 respectively.